Title

Author

Date Thesis Awarded

Document Type

Honors Thesis

Degree Name

Bachelors of Science (BS)

Department

Mathematics

Advisor

Chi-Kwong Li

Committee Member

Sarah Day

Committee Member

Jianjun Paul Tian

Committee Member

Margaret Somosi Saha

Abstract

The genetic code-based matrices constructed in this work and the corresponding hamming distance matrices are studied using combinatorics and linear algebra approaches. Recursive schemes for generating the matrices are obtained. Algebraic properties such as ranks, eigenvalues, and eigenvectors of the Hamming distance matrices are examined. The results lead to an easy calculation of the powers of the Hamming distance matrices. Moreover, a decomposition of the Hamming Distance matrices in terms of permutation matrices is obtained. The decomposition gives rise to hypercube structures to the genetic code based matrices. A new scheme is given to generate matrices where each entry is a 4-tuple, which counts the number of each nucleotide in the entries of the genetic code matrix. Connections and potential applications of the results will be discussed.